Finite Group Databasebeta

← #17949971

Subgroups — #17949971

Order 4352.

456 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14544700C212yesmaximal
2#14543605C214yesmaximal
3#14531351C211yesmaximal, characteristic
4C2×#10587544—22no—
5#11763675—22no—
6#11763675C2214yes—
7C2×#10587555C411yescharacteristic
8C2×#10587573C412yes—
9#11762714C2212yes—
10#11762705—22no—
11C4⋊C4×Dic17—22no—
12C42×Dic17C2211yescharacteristic
13C17×#384C411yescharacteristic
14C22×Dic34C2×C412yes—
15C22×#3624—24no—
16C2×C4⋊C4×C17—22no—
17C2×C4⋊C4×C17C2×C412yes—
18C2×C42×C17C2×C411yescharacteristic
19C2×C4⋊Dic17—22no—
20C2×#63225—22no—
21C2×C4×Dic17—22no—
22C2×C4×Dic17C2×C411yescharacteristic
23C2×C4×Dic17D412yes—
24C2×C4×Dic17D412yes—
25C2×C4×Dic17C2311yescharacteristic
26#10587573—44no—
27#10587555—24no—
28#10587544—44no—
29#10587502—24no—
30C22×C4×C17—22no—
31C22×C4×C17C22⋊C412yes—
32C22×C4×C17C22×C411yescharacteristic
33C22×Dic17—22no—
34C22×Dic17C22⋊C411yescharacteristic
35C22×Dic17C22⋊C411yescharacteristic
36C22×Dic17C2×D412yes—
37C2×Dic34—22no—
38C2×Dic34—42no—
39C2×Dic34—42no—
40C2×Dic34M1614yes—
41C2×#3624—44no—
42C2×#3624—44no—
43C2×#3624—44no—
44C4⋊C4×C17—42no—
45C4⋊C4×C17—44no—
46C42×C17—22no—
47C4⋊Dic17—28no—
48#63225—44no—
49C4×Dic17—22no—
50C4×Dic17—42no—
51C4×Dic17—41no—
52C4×Dic17—44no—
53C4×Dic17SD1614yes—
54C4×Dic17Q1614yes—
55#7653—171nomaximal, Sylow
56C23×C17C2×C22⋊C411yescharacteristic
57C2×C4×C17—22no—
58C2×C4×C17—21no—
59C2×C4×C17—21no—
60C2×C4×C17—22no—
61C2×C4×C17—42no—
62C2×C4×C17—44no—
63C2×C4×C17#10314yes—
64C2×C4×C17C2×M1612yes—
65C2×Dic17—22no—
66C2×Dic17—22no—
67C2×Dic17—24no—
68C2×Dic17—21no—
69C2×Dic17—22no—
70C2×Dic17—42no—
71C2×Dic17—42no—
72C2×Dic17#10012yes—
73C2×Dic17#10314yes—
74C2×Dic17C2×SD1612yes—
75C2×Dic17C2×Q1612yes—
76Dic34—44no—
77Dic34—44no—
78#3624—84no—
79C4×C4⋊Q8—171no—
80#1831—172no—
81#1272—174no—
82C22×C17#40711yescharacteristic
83C22×C17#41011yescharacteristic
84C22×C17C2×#10011yescharacteristic
85C22×C17C2×#10312yes—
86C22×C17#42112yes—
87C4×C17—22no—
88C4×C17—24no—
89C4×C17—82no—
90Dic17—22no—
91Dic17—22no—
92Dic17—41no—
93Dic17—44no—
94Dic17#33314yes—
95C2×C4⋊Q8—171no—
96C2×C4×Q8—172no—
97C2×C4⋊C8—342no—
98#391—172no—
99#389—342no—
100#384#59511yescharacteristic
101C4×C4⋊C4—342no—
102C43—171no—
103#336—174no—
104#336—342no—
105C2×C17#146611yescharacteristic
106C2×C17#148712yes—
107C2×C17#151812yes—
108C2×C17#153611yescharacteristic
109C2×C17C2×#33311yescharacteristic
110C22×Q8—172no—
111C22×C8—344no—
112C4⋊Q8—344no—
113C4×Q8—684no—
114C2×C4⋊C4—22no—
115C2×C4⋊C4—342no—
116C2×C4⋊C4—342no—
117C2×C4⋊C4C2×#59512yes—
118C2×C42—172no—
119C2×C42—171no—
120C2×C42—172no—
121C2×C42—171no—
122C2×C42—342no—
123C2×C42C2×#59511yescharacteristic
124C4⋊C8—684no—
125#95—344no—
126C17#765311yescharacteristic, complemented, Sylow
127C2×Q8—174no—
128C2×Q8—342no—
129C2×Q8—682no—
130C2×Q8—682no—
131C22×C4—22no—
132C22×C4—171no—
133C22×C4—172no—
134C22×C4—171no—
135C22×C4—342no—
136C22×C4C22⋊#59512yes—
137C22×C4C22×#59511yescharacteristic
138C2×C8—684no—
139C2×C8—684no—
140C2×C8—684no—
141C4⋊C4—42no—
142C4⋊C4—44no—
143C4⋊C4—348no—
144C4⋊C4—684no—
145C42—22no—
146C42—174no—
147C42—174no—
148C42—342no—
149C42—681no—
150C42—682no—
151C42—684no—
152C23C2×C22⋊#59511yescharacteristic
153Q8—684no—
154Q8—684no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—42no—
160C2×C4—44no—
161C2×C4—172no—
162C2×C4—174no—
163C2×C4—172no—
164C2×C4—172no—
165C2×C4—342no—
166C2×C4—342no—
167C2×C4—344no—
168C2×C4—341no—
169C2×C4—342no—
170C2×C4—682no—
171C2×C4—682no—
172C2×C4#1058754914yes—
173C2×C4D17⋊M1612yes—
174C8—1364no—
175C22#1176378111yescharacteristic
176C22#1176379011yescharacteristic
177C22D17⋊#10011yescharacteristic
178C22C2×#1058754912yes—
179C22#1176380712yes—
180C4—22no—
181C4—24no—
182C4—82no—
183C4—174no—
184C4—342no—
185C4—342no—
186C4—681no—
187C4—684no—
188C2#1454404511yescharacteristic
189C2#1454411412yes—
190C2#1454421612yes—
191C2#1454427311yescharacteristic
192C2D17⋊#33311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#384C4
socle, prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4×Dic17C23
hypercenter#384#595
hypocenterC17#7653
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
126. C17#7653semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145447002
#145436052
#145313512
#765317